Write the complex equation 8 + 3i in trigonometric form

z = 8.544[cos (20.6) + isin (20.6) }

Step-by-step explanation:

Given

8 + 3i

Required

Rewrite in trigonometric form.

The trigonometric form of a complex equation is

z = r[cosθ + isinθ]

Let a = 3 and b = 8

Where

r is calculated by

r² = b² + a²

And

θ is calculated by

θ = arctan (a/b)

Substituting 3 for a and 8 for b

r² = a² + b² becomes

r² = 3² + 8²

r² = 9 + 64

r² = 73

√r² = √73

r = √73

r = 8.544

Calculating θ

θ = arctan (a/b) becomes

θ = arctan (3/8)

θ = arctan (0.375)

θ = 20.556°

θ = 20.6 - - - Approximated

Hence, z = r[cosθ + isinθ] becomes

z = 8.544[cos (20.6) + isin (20.6) }